IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2017cf1047.html
   My bibliography  Save this paper

Anticipated Backward SDEs with Jumps and Quadratic-Exponential Growth Drivers

Author

Listed:
  • Masaaki Fujii

    (Faculty of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

Abstract

In this paper, we study a class of Anticipated Backward Stochastic Differential Equa- tions (ABSDE) with jumps. The solution of the ABSDE is a triple (Y,Z,ψ) where Y is a semimartingale, and (Z,ψ) are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of Y’s future paths, as well as quadratic and exponential growth on the spot values of (Z,ψ), respectively. The existence of the unique solution is proved for Markovian and non-Markovian settings with different structural assumptions on the driver. In the former case, some regularities on (Z,ψ) with respect to the forward process are also obtained.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2017. "Anticipated Backward SDEs with Jumps and Quadratic-Exponential Growth Drivers," CIRJE F-Series CIRJE-F-1047, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2017cf1047
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2017/2017cf1047.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Antonelli, Fabio & Mancini, Carlo, 2016. "Solutions of BSDE’s with jumps and quadratic/locally Lipschitz generator," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3124-3144.
    2. Olivier Menoukeu Pamen, 2015. "Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 998-1031, December.
    3. Morlais, Marie-Amelie, 2010. "A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1966-1995, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Masaaki Fujii & Akihiko Takahashi, 2018. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers (Revised version of F-409)," CARF F-Series CARF-F-431, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Masaaki Fujii & Akihiko Takahashi, 2017. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers," CARF F-Series CARF-F-409, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Masaaki Fujii & Akihiko Takahashi, 2017. "Anticipated Backward SDEs with Jumps and Quadratic-Exponential Growth Drivers," CIRJE F-Series CIRJE-F-1047, CIRJE, Faculty of Economics, University of Tokyo.
    4. Masaaki Fujii & Akihiko Takahashi, 2017. "Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers," Papers 1705.02440, arXiv.org, revised Jul 2018.
    5. Fujii, Masaaki & Takahashi, Akihiko, 2018. "Quadratic–exponential growth BSDEs with jumps and their Malliavin’s differentiability," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2083-2130.
    6. Masaaki Fujii & Akihiko Takahashi, 2016. "Quadratic-exponential growth BSDEs with Jumps and their Malliavin’s Differentiability (revised version of CARF-F-376)," CARF F-Series CARF-F-395, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Marina Santacroce & Paola Siri & Barbara Trivellato, 2023. "Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models," Papers 2302.08253, arXiv.org.
    8. Masaaki Fujii & Akihiko Takahashi, 2017. "Quadratic-exponential growth BSDEs with Jumps and their Malliavin's Differentiability (Forthcoming in Stochastic Processes and their Applications)(revised version of CARF-F-395)," CARF F-Series CARF-F-420, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Tiago Roux Oliveira & Victor Hugo Pereira Rodrigues & Miroslav Krstić & Tamer Başar, 2021. "Nash Equilibrium Seeking in Quadratic Noncooperative Games Under Two Delayed Information-Sharing Schemes," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 700-735, December.
    10. Masaaki Fujii, 2019. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CIRJE F-Series CIRJE-F-1133, CIRJE, Faculty of Economics, University of Tokyo.
    11. Richter, Anja, 2014. "Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3578-3611.
    12. Olivier Menoukeu-Pamen & Romuald Hervé Momeya, 2017. "A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 349-388, June.
    13. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    14. Ying Hu & Xiaomin Shi & Zuo Quan Xu, 2022. "Optimal consumption-investment with coupled constraints on consumption and investment strategies in a regime switching market with random coefficients," Papers 2211.05291, arXiv.org.
    15. Masaaki Fujii & Akihiko Takahashi, 2015. "Quadratic-exponential growth BSDEs with Jumps and their Malliavin's Differentiability," Papers 1512.05924, arXiv.org, revised Sep 2017.
    16. Masaaki Fujii, 2019. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-467, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    17. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    18. Dirk Becherer & Martin Buttner & Klebert Kentia, 2016. "On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples," Papers 1607.06644, arXiv.org, revised Nov 2019.
    19. Kunz, Andreas & Popp, Markus, 2021. "Economic Neutral Position: How to best replicate not fully replicable liabilities?," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 53-67.
    20. Masaaki Fujii & Akihiko Takahashi, 2015. "Quadratic-exponential growth BSDEs with Jumps and their Malliavin’s Differentiability," CARF F-Series CARF-F-376, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2017cf1047. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.